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The week began with the breaking of the siege of Mount Sinjar in Iraq, thanks to US bombing, and ended with the public beheading of journalist James Foley in Syria and renewed Russian aggression in Ukraine.

The juxtaposition of military success and public human failure has caused a sense of whiplash around US President Barack Obama's foreign policy and further stoked the debate about his world view.

Obama's detractors revived criticism that his foreign policy was based on retreat from the world, typified by the withdrawal of US forces from Iraq three years ago, a lack of direct action in Syria and an economics-first approach to driving Russia's military back from Ukraine.

His supporters argue his approach has been consistent with his strategy of returning the US to a foreign policy built around economic engagement rather than military intervention. The question is whether he is contradicting his pledge in his 2009 Nobel Prize lecture "to face the world as it is", not as he would like it to be.

"He thought he could change the tenor more easily than he could, and I think he thought the world would be more responsive to his desires than the world has proven to be," said Jon Alterman, senior vice-president of the Centre for Strategic and International Studies. "Now he faces the criticism that … he embarks on a series of skirmishes that are reactive and not of his choosing."

In place of large military deployments, Obama has relied on smaller operations to manage, rather than resolve, many of the conflicts that have arisen. The attempted rescue of Foley earlier this year from a camp deep inside Syria stands as the most recent example of that approach.

But smaller has not translated into peace or greater American influence. After pulling troops from Iraq, Obama is now overseeing a military operation to protect Iraqis threatened by the Islamic State, secure US personnel in Kurdish Iraq, and advise the country's US-trained army.

The question of how to roll back the Islamic State's territorial gains is one that he and the Pentagon must deal with. However, administration officials say they are unwilling to sacrifice either of Obama's guiding principles.

"Iraq and Syria are very much within the goal of preventing the threat of terrorism from emanating from outside the United States," Ben Rhodes, deputy national security adviser, said last week. "That's a core interest."

At the same time, he said, Obama was not reconsidering his view that Iraq - and Afghanistan - must be primarily responsible for their own security.

While Obama and his advisers see consistency in his actions, observers see more of a patchwork. "This president has ignored the threat for a long period of time, and now we're paying the price," Republican senator John McCain told the Arizona Republic.

Even former secretary of state Hillary Rodham Clinton said recently that "Don't do stupid stuff" - the president's latest foreign policy credo - was not an "organising principle".

"The problem for Obama is he often sets up these false choices between essentially doing nothing and sending in the 82nd Battalion," said David Kramer, a senior State Department official in the George W. Bush administration. "And there are gradations about what one can do, including providing military support to forces that we should be supporting."

Obama has also drawn flak for enjoying a two-week holiday amid the various problems.

Adding to the challenges has been the crisis in Ukraine, which has wounded US relations with Russia, and the conflict in Gaza. Officials say Obama has put a lot on the line in both places.

But current and former administration officials see a big difference between what's happening in Iraq and Syria and what's happening in Ukraine and Gaza. The former fit into a framework of potentially threatening Americans. Solving the latter crises appeals to US principles of democracy and diplomacy, but they do not pose direct threats.

15 days on Martha’s Vineyard: apart from two days of Washington meetings last week, the president has been enjoying the island since August 9.

9 rounds of golf: the most notable activity of Obama’s holiday, which brought criticism from some and defence from others.

3 press statements: Obama addressed the travelling White House press corps twice the first week and again last Wednesday, covering Iraq’s elections, the unrest in Ferguson, and journalist James Foley’s killing.

2 beach visits: the president, first lady and their daughters went to a beach in Edgartown.

1 fundraiser: Obama hosted a fundraiser at the home of Roger Brown and Linda Mason.

1 hike, bike ride, fireworks display: Obama, his wife Michelle and daughter Malia took a bike ride through the woods. He and his wife went for a morning hike in the Chilmark woods. The Obamas also took in the annual Oak Bluffs fireworks show.